Graph Algorithms and Graph Measures for the Life Sciences Falk - PowerPoint PPT Presentation

Graph Algorithms and Graph Measures for the Life Sciences Falk Schreiber 23/10/2014 1

Networks and Graphs in the Life Sciences � Graph � Network

Network Representation � Network is an informal description for a set of elements with connections or interactions between them and data attached to them � Graph is a formal description, it is a mathematical object consisting of vertices and edges representing elements and connections, respectively

Interactions à Networks à Pathways � A collection of interactions and/or transformations defines a network � Pathways are subsets of networks � All pathways are networks, however not all networks are pathways � Difference: level of annotation/understanding � We can define a pathway as a biological network that relates to a known physiological process or phenotype � There is no precise biological definition of a pathway � Partitioning of networks into pathways is somewhat arbitrary

Networks a Decade Ago

Can you Spot the Error? [from Milo et al., Science, 2002]

Retraction and Impact Factor

Just an Example …

From Biological Building Blocks to Complex Systems Genome � Set of hereditary instructions needed to build, run and maintain a particular organism Genes Transcripts Proteins Metabolites

From Biological Building Blocks to Complex Systems Transcriptome � Set of RNA transcribed from genes within the genome by a particular cell at a particular time � Depends on the tissue, the developmental stage of the organism and the metabolic state of the cell Genes Transcripts Proteins Metabolites

From Biological Building Blocks to Complex Systems Proteome � Set of proteins translated from RNA within a transcriptome by a particular cell at a particular time � Complete proteome of a cell: set of all potential proteins that could be synthesised by the cell Genes Transcripts Proteins Metabolites

From Biological Building Blocks to Complex Systems Metabolome � Set of all the metabolites inside a particular cell at a particular time Genes Transcripts Proteins Metabolites

From Biological Building Blocks to Complex Systems Genes Transcripts Proteins Metabolites

From Biological Building Blocks to Complex Systems 20th century biology (reductionist approach) Phenylketonuria is caused by a mutated gene for the enzyme phenylalanine hydroxylase (PAH) Genes Transcripts Proteins Metabolites

From Biological Building Blocks to Complex Systems 20th century biology 21th century biology (reductionist approach) (integrative approach) Cancer, heart diseases, … multiple, complex changes Genes Transcripts Proteins Metabolites

From Biological Building Blocks to Complex Systems Genes Transcripts Proteins Metabolites

Biological Pathways and Networks - Examples � Signal transduction pathway and networks � Cellular processes that recognize extra- or intra-cellular signals and induce appropriate cellular responses � Gene regulatory networks � Pathways that regulate a cell’s behaviors, including transcription and translation � Metabolic pathway � A series of enzymatic reactions that produce a specific product � Protein interaction networks � Interaction of proteins (e.g. activation, non-covalent binding)

Biological Pathways and Networks chromosome protein clustering location of genes level 2 State-of-the-Art Andreas Kerren Helen C. Purchase Matthew O. Ward (Eds.) Survey level 1 LNCS 8380 Multivariate Network Visualization gene regulation protein interaction metabolism Dagstuhl Seminar #13201 Dagstuhl Castle, Germany, May 12–17, 2013 Revised Discussions 123

Many Informatics Areas Health informatics/ � Evolutionary networks Environmental informatics � Infection networks � Ecological networks / food webs � Neuronal networks Medical informatics � Hormonal networks � Signalling networks � Gene regulatory network Bioinformatics � Protein interaction networks � Metabolic networks � Chemical structure graphs Chemoinformatics

Network Usage - Examples Representation/exploration Network analysis Data context/analysis Simulation

Network Analysis - Network Centralities � Centrality of graph G=(V,E) � Funktion c:V → R � With c(u)>c(v) , if u ∈ V more important than v ∈ V � Ranking of vertices � According to importance � Based on the network structure � Application examples � Hypothesis generation for experiments � Which patients should be vaccinated first � Problem [from Jeong et al., Nature, 2001] � Works not well with existing algorithms

New Centrality Measure Based on network motifs � Sub-graphs representing patterns of local interconnections � May represent basic building blocks and design patterns of functional modules [from Babu et al., Current Opinion in Structural Biology, 2004]

Motifs in Gene Regulatory Networks: Feed-forward Loop Example of functional properties � Noise filtering: responds only to persistent activations [from Shen-Orr et al., Nature Genetics, 2002]

Motif-based Centrality � Combines centrality measures and network motifs � Uses occurrences of a motif in the network � Incorporates functional substructures into centrality analysis � { ~ G G G G G M } = ⊆ ∧ − M M M M { � c ( v ) G G G v V ( G ) } | = ∈ ∧ ∈ M M M M vertex centrality v2 3 v3 2 v4 2 v1 1 v5 1 Motif (Feed-forward loop) Target graph M G

Motif-based Centrality with Roles � Different vertices have different roles � Count number of matches according to roles � { ~ G G G G G M } = ⊆ ∧ − M M M M { � c ( v , r ) G G G v V ( G ) role ( v , G ) r } | = ∈ ∧ ∈ ∧ = M M M M M vertex centrality A B C v1 1 0 0 v2 2 1 0 v3 0 1 1 v4 0 0 2 v5 0 1 0 Motif (Feed-forward loop) Target graph M G

Gene Regulatory Network of E. coli � Based on data from RegulonDB (http://regulondb.ccg.unam.mx/) � 1250 vertices and 2515 edges � Global regulators?

Motif-based Centrality with Roles for E. coli gene centrality A B C crp 254 0 0 fnr 150 53 0 ihfAB 61 0 0 arcA 58 53 0 fis 40 70 0 modE 18 0 0 soxS 18 1 0 hns 14 39 0 � Top 20 genes (of 1250) fhlA 11 0 0 gadE 11 0 0 � 11 of 18 global regulators cpxR 11 0 0 (Martínez-Antonio and rob 10 0 0 Collado-Vides) galR 8 0 0 gadX 8 26 0 gntR 6 0 0 � Method works also for fur 6 36 1 other networks oxyR 6 1 0 � Even better results with tdcR 6 0 0 srlR 5 11 1 different motifs narL 5 95 0

Two Vague Ideas � Are scale-free and small- world networks relevant or more an artifact ? THEINTERNET, mapped on the opposite page, is a scale-free network in that some siteS (starbursts and detail above) have a seemingly unlimited number of connections to other sites. This map, made on February 6, 2003, traces the shortest routes from atest WebsinHo about 100,000 others, using like colors for similar Webaddresses. a - Scientistshaverecentlydiscoveredthat variouscomplexsystemshave antlnderlyihg~..'~tJ;i~e~tu"eg~Ye'l"rne(;lb9.$ha redorga nili ngprincipies. Thisinsight has important impli~ationsfor a hostof applications, fromdrugdevelopment to Internetsecurity BYALBERT-U\SZLO BARABASI ANDERICBONABEAU 50 SCIENTIFIC AMERICAN MAY 2003

Degree Distribution - Examples

Models for Networks of Complex Topology � Erd ő s-Rényi (1960) � Watts-Strogatz (1998) � Barabási-Albert (1999)

The Erd ő s-Rényi [ER] Model (1960) � Start with n nodes and 0 edges � Connect each pair of vertices with probability p ER � Many properties in these graphs appear quite suddenly, at a threshold value of p ER � If p ER ~c/n with c<1, then almost all nodes belong to isolated trees

The Watts-Strogatz [WS] Model (1998) � Start with a regular network with n nodes � Rewire each edge with probability p � For p=0 (regular networks) � High clustering coefficient C , high characteristic path length L � For p=1 (random networks) � Low clustering coefficient C, low characteristic path length L

The Watts-Strogatz [WS] Model (1998) � There is a broad interval of p for which characteristic path length L is small but clustering coefficient C remains large � Small world networks are common

The Barabási-Albert [BA] Model (1999) � Look at the distribution of degrees k � A scale-free network is a network where small proportion of the nodes have high degree of connection ("highly connected hubs“) � The probability of finding a highly connected node decreases exponentially with k � p(k) ~ k - γ , a given node has k connections to other nodes with probability as the power law distribution with γ = [2, 3]

The Barabási-Albert [BA] Model (1999)

Protein Interaction Networks � Also other networks, e.g. transcript correlation networks

Two Vague Ideas � Are scale-free and small-world networks relevant or more an artifact ? � Taxonomy for centrality measures

Taxonomy for Centrality Measures